ALBERT

Description: Quantifying the hydraulic properties of single fractures is a fundamental requirement to understand fluid flow in fractured reservoirs. For an ideal planar fracture, the effective flow is proportional to the cube of the fracture aperture. In contrast, real fractures are rarely planar, and correcting the cubic law in terms of fracture roughness has therefore been a subject of numerous studies in the past. Several empirical relationships between hydraulic and mechanical aperture have been proposed based on statistical variations of the aperture field. However, often, they exhibit non-unique solutions, attributed to the geometrical variety of naturally occurring fractures. In this study, a non-dimensional fracture roughness quantification scheme is acquired, opposing effective surface area against relative fracture closure. This is used to capture deviations from the cubic law as a function of quantified fracture roughness, here termed hydraulic efficiencies. For that, we combine existing methods to generate synthetic 3-D fracture voxel models. Each fracture consists of two random, 25 cm2 wide self-affine surfaces with prescribed roughness amplitude, scaling exponent, and correlation length, which are separated by varying distances to form fracture configurations that are broadly spread in the newly formed two-parameter space (mean apertures in submillimeter range). First, we performed a percolation analysis on 600 000 synthetic fractures to narrow down the parameter space on which to conduct fluid flow simulations. This revealed that the fractional amount of contact and the percolation probability solely depend on the relative fracture closure. Next, Stokes flow calculations are performed, using a 3-D finite differences code on 6400 fracture models to compute directional permeabilities. The deviations from the cubic law prediction and their statistical variability for equal roughness configurations were quantified. The resulting 2-D solution fields reveal decreasing cubic law accordance down to 1 % for extreme roughness configurations. We show that the non-uniqueness of the results significantly reduces if the correlation length of the aperture field is much smaller than the spatial extent of the fracture. An equation was provided that predicts the average behavior of hydraulic efficiencies and respective fracture permeabilities as a function of their statistical properties. A model to capture fluctuations around that average behavior with respect to their correlation lengths has been proposed. Numerical inaccuracies were quantified with a resolution test, revealing an error of 7 %. By this, we propose a revised parameterization for the permeability of rough single fractures, which takes numerical inaccuracies of the flow calculations into account. We show that this approach is more accurate compared to existing formulations. It can be employed to estimate the permeability of fractures if a measure of fracture roughness is available, and it can readily be incorporated in discrete fracture network modeling approaches.

Description: We apply three-dimensional (3-D) thermo-mechanical numerical simulations of the shortening of the upper crustal region of a passive margin in order to investigate the control of 3-D laterally variable inherited structures on fold-and-thrust belt evolution and associated nappe formation. We consider tectonic inheritance by employing an initial model configuration with basement horst and graben structures having laterally variable geometry and with sedimentary layers having different mechanical strength. We use a visco-plastic rheology with a temperature-dependent flow law and a Drucker–Prager yield criterion. The models show the folding, detachment (shearing off) and horizontal transport of sedimentary units, which resemble structures of fold and thrust nappes. The models further show the stacking of nappes. The detachment of nappe-like structures is controlled by the initial basement and sedimentary layer geometry. Significant horizontal transport is facilitated by weak sedimentary units below these nappes. The initial half-graben geometry has a strong impact on the basement and sediment deformation. Generally, deeper half-grabens generate thicker nappes and stronger deformation of the neighbouring horst, while shallower half-grabens generate thinner nappes and less deformation in the horst. Horizontally continuous strong sediment layers, which are not restricted to initial graben structures, cause detachment (décollement) folding and not overthrusting. The amplitude of the detachment folds is controlled by the underlying graben geometry. A mechanically weaker basement favours the formation of fold nappes, while stronger basement favours thrust sheets. The model configuration is motivated by applying the 3-D model to the Helvetic nappe system of the Central Alps of France and Switzerland. Our model reproduces several first-order features of this nappe system, namely (1) closure of a half-graben and associated formation of the Morcles and Doldenhorn nappes, (2) overthrusting of a nappe resembling the Wildhorn and Glarus nappes, and (3) formation of a nappe pile resembling the Helvetic nappes resting above the Infrahelvetic complex. Furthermore, the finite strain pattern, temperature distribution and timing of the 3-D model is in broad agreement with data from the Helvetic nappe system. Our model, hence, provides a 3-D reconstruction of the first-order tectonic evolution of the Helvetic nappe system. Moreover, we do not apply any strain softening mechanisms. Strain localization, folding and nappe transport are controlled by initial geometrical and mechanical heterogeneities showing the fundamental importance of tectonic inheritance on fold-and-thrust belt evolution.

Description: The flow of fluids through porous media such as groundwater flow or magma migration are key processes in geological sciences. Flow is controlled by the permeability of the rock, thus an accurate determination and prediction of its value is of crucial importance. For this reason, permeability has been measured across different scales. As laboratory measurements exhibit a range of limitations, the numerical prediction of permeability at conditions where laboratory experiments struggle has become an important method to complement laboratory approaches. At high resolutions, this prediction becomes computationally very expensive, which makes it crucial to develop methods that maximize accuracy. In recent years, the flow of non-Newtonian fluids through porous media has gained additional importance due to e.g., the use of nanofluids for enhanced oil recovery. Numerical methods to predict fluid flow in these cases are therefore required. Here, we employ the open-source finite difference solver LaMEM to numerically predict the permeability of porous media at low Reynolds numbers for both Newtonian as well as non-Newtonian fluids. We employ a stencil rescaling method to better describe the solid-fluid interface. The accuracy of the code is verified by comparing numerical solutions to analytical ones for a set of simplified model setups. Results show that stencil rescaling significantly increases the accuracy at no additional computational cost. Finally, we use our modeling framework to predict the permeability of a Fontainebleau sandstone, and demonstrate numerical convergence. Results show very good agreement with experimental estimates as well as with previous studies. We also demonstrate the ability of the code to simulate the flow of power law fluids through porous media. As in the Newtonian case, results show good agreement with analytical solutions.

Description: The flow of fluids through porous media such as groundwater flow or magma migration is a key process in geological sciences. Flow is controlled by the permeability of the rock; thus, an accurate determination and prediction of its value is of crucial importance. For this reason, permeability has been measured across different scales. As laboratory measurements exhibit a range of limitations, the numerical prediction of permeability at conditions where laboratory experiments struggle has become an important method to complement laboratory approaches. At high resolutions, this prediction becomes computationally very expensive, which makes it crucial to develop methods that maximize accuracy. In recent years, the flow of non-Newtonian fluids through porous media has gained additional importance due to, e.g., the use of nanofluids for enhanced oil recovery. Numerical methods to predict fluid flow in these cases are therefore required. Here, we employ the open-source finite difference solver LaMEM (Lithosphere and Mantle Evolution Model) to numerically predict the permeability of porous media at low Reynolds numbers for both Newtonian and non-Newtonian fluids. We employ a stencil rescaling method to better describe the solid–fluid interface. The accuracy of the code is verified by comparing numerical solutions to analytical ones for a set of simplified model setups. Results show that stencil rescaling significantly increases the accuracy at no additional computational cost. Finally, we use our modeling framework to predict the permeability of a Fontainebleau sandstone and demonstrate numerical convergence. Results show very good agreement with experimental estimates as well as with previous studies. We also demonstrate the ability of the code to simulate the flow of power-law fluids through porous media. As in the Newtonian case, results show good agreement with analytical solutions.